In the given figure, B is an obtuse angle, if M and N are the mid-points of AB and AC respectively, then AN is always greater than

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Solution

The correct option is C AM
Given that M and N are mid-points of AB and AC respectively.
By mid-point theorem, CB || NM.
∴ ∠ABC = ∠AMN (Corresponding angles)
Thus, ∠AMN is an obtuse angle, as B is an obtuse angle.
In a triangle, side opposite to the largest angle is the longest.
∴ AN > AM and AN > MN
Hence, the correct answer is option (c).

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